1
GATE EE 2018
Numerical
+1
-0.33
The series impedance matrix of a short three-phase transmission line in phase coordinates is $$\left[ {\matrix{ {{Z_s}} & {{Z_m}} & {{Z_m}} \cr {{Z_m}} & {{Z_s}} & {{Z_m}} \cr {{Z_m}} & {{Z_m}} & {{Z_s}} \cr } } \right]$$.

If the positive sequence impedance is (1 + 𝑗 10) $$\Omega$$, and the zero sequence is (4 + 𝑗 31) $$\Omega$$, then the imaginary part of Zm (in $$\Omega$$) is ______(up to 2 decimal places).
2
GATE EE 2018
+2
-0.67
The positive, negative and zero sequence impedances of a three phase generator are Z1, Z2 and Z0 respectively. For a line-to-line fault with fault impedance Zf, the fault current is If1 = kIf, where If is the fault current with zero fault impedance. The relation between Zf and k is
A
$${Z_f} = {{\left( {{Z_1} + {Z_2}} \right)\left( {1 - k} \right)} \over k}$$
B
$${Z_f} = {{\left( {{Z_1} + {Z_2}} \right)\left( {1 + k} \right)} \over k}$$
C
$${Z_f} = {{\left( {{Z_1} + {Z_2}} \right)k} \over {1 - k}}$$
D
$${Z_f} = {{\left( {{Z_1} + {Z_2}} \right)k} \over {1 + k}}$$
3
GATE EE 2018
Numerical
+1
-0.33
The positive, negative and zero sequence impedances of a 125 MVA, three-phase, 15.5 kV, star-grounded, 50 Hz generator are 𝑗0.1 pu, j0.05 pu and j0.01 pu respectively on the machine rating base. The machine is unloaded and working at the rated terminal voltage. If the grounding impedance of the generator is j0.01 pu, then the magnitude of fault current for a b-phase to ground fault (in kA) is __________ (up to 2 decimal places).
4
GATE EE 2018
+1
-0.33
Consider a lossy transmission line with V1 and V2 as the sending and receiving end voltages, respectively. Z and X are the series impedance and reactance of the line, respectively. The steady-state stability limit for the transmission line will be
A
greater than $$\left| {{{{V_1}{V_2}} \over X}} \right|$$
B
less than $$\left| {{{{V_1}{V_2}} \over X}} \right|$$
C
equal to $$\left| {{{{V_1}{V_2}} \over X}} \right|$$
D
equal to $$\left| {{{{V_1}{V_2}} \over Z}} \right|$$
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